What is involved in the substitution method for solving equations?

The substitution method for solving equations involves expressing one variable in terms of another variable within a system of equations. In this approach, you typically start with a set of two equations. You solve one of the equations for one variable (say ( x ) or ( y )) and then substitute that expression into the other equation. This allows you to reduce the problem to one variable, making it easier to find the solution.

For example, if you have two equations, ( y = 2x + 3 ) and ( x + y = 10 ), you can substitute the expression for ( y ) from the first equation into the second equation. This method simplifies the solving process and leads you directly to the values of both variables once you back-substitute.

Utilizing substitution is particularly beneficial in cases where one equation is already solved for one variable, making it very straightforward to implement. This method highlights the interdependence of the variables and is a fundamental technique used in algebra to find solutions systematically.